TY - JOUR

T1 - CANONICAL and n-CANONICAL MODULES of A NOETHERIAN ALGEBRA

AU - Hashimoto, Mitsuyasu

N1 - Publisher Copyright:
© 2016 by The Editorial Board of the Nagoya Mathematical Journal.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We define canonical and -canonical modules of a module-finite algebra over a Noether commutative ring and study their basic properties. Using n-canonical modules, we generalize a theorem on (n, C)-syzygy by Araya and Iima which generalize a well-known theorem on syzygies by Evans and Griffith. Among others, we prove a noncommutative version of Aoyama's theorem which states that a canonical module descends with respect to a flat local homomorphism.

AB - We define canonical and -canonical modules of a module-finite algebra over a Noether commutative ring and study their basic properties. Using n-canonical modules, we generalize a theorem on (n, C)-syzygy by Araya and Iima which generalize a well-known theorem on syzygies by Evans and Griffith. Among others, we prove a noncommutative version of Aoyama's theorem which states that a canonical module descends with respect to a flat local homomorphism.

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U2 - 10.1017/nmj.2016.44

DO - 10.1017/nmj.2016.44

M3 - Article

AN - SCOPUS:85020639880

SN - 0027-7630

VL - 226

SP - 165

EP - 203

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

ER -